Impedance of an Encircling Coil due to a Cylindrical Tube with Varying Properties

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functions of complex order.




References:
[1] N. Burais, and A. Nicolas, "Electromagnetic field analysis in remote
field eddy current testing systems", IEEE Trans. Magn., vol. 25, pp.
3010-3012, 1989.
[2] C. Reboud, D. Prémel, D. Lesselier, and B. Bisiaux, "Recent advances
in simulation of eddy current testing of tubes and experimental
validations", Review of Quantitative Nondestructive Evaluation, vol.
26, pp. 241-248, 2007
[3] V. Monebhurrun, B. Duchêne, and D. Lesselier, "Three-dimensional
inversion of eddy current data for nondestructive evaluation of steam
generator tubes", Inverse Problems, vol. 14, pp. 707-724, 1998.
[4] J.F.P.J. Abascal, M. Lambert, D. Lesselier, and O. Dorn, "3D eddy
current imaging of metal tubes by gradient-based, controlled evolution
of level sets", IEEE Trans. Magn., vol. 44, pp. 4721-4729, 2008.
[5] C.V. Dodd, and W.E. Deeds, "Analytical solutions to eddy-current
probe-coil problems", J. Appl. Phys., vol. 39, pp. 2829-2838, 1968.
[6] C.V. Dodd, W.E. Deeds, and J.W. Luquire, "Integral solutions to some
eddy current problems", Int. J. Nondestructive Testing, vol. 1, pp. 29-
107, 1969.
[7] C.V. Dodd, C.C. Cheng, and W.E. Deeds, "Induction coils coaxial with
an arbitrary number of cylindrical conductors", J. Appl. Phys., vol. 45,
pp. 638-647, 1974.
[8] J.R. Bowler, and T.P. Theodoulidis, "Eddy currents induced in a
conducting rod of finite length by a coaxial encircling coil", J. Phys.
D: Appl. Phys., vol. 38, pp. 2861-2868, 2005.
[9] C.-C. Tai, H.-C. Yang, and Y.-H. Liu, "Modeling the surface condition
of ferromagnetic metal by the swept-frequency eddy current method",
IEEE Trans. Magn., vol. 38, pp. 205-210, 2002.
[10] C.-C. Tai, "Characterization of coatings on magnetic metal using the
swept-currency eddy current method", Rev. Sci. Instr., vol. 71, pp.
3161-3167, 2000.
[11] M.Ya. Antimirov, A.A. Kolyshkin, and R. Vaillancourt, Mathematical
models for eddy current testing. Montreal: CRM, 1997.
[12] A.D. Polyanin, and V.F. Zaitsev, Handbook of exact solutions for
ordinary differential equations . Florida: Chapman&Hall/CRC, 2003.